On operators with the same spectrum
Gh. Constantin (1975)
Matematički Vesnik
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Gh. Constantin (1975)
Matematički Vesnik
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J. Janas (1988)
Colloquium Mathematicae
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Marcin Bownik, John Jasper (2015)
Bulletin of the Polish Academy of Sciences. Mathematics
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Given a finite set X⊆ ℝ we characterize the diagonals of self-adjoint operators with spectrum X. Our result extends the Schur-Horn theorem from a finite-dimensional setting to an infinite-dimensional Hilbert space analogous to Kadison's theorem for orthogonal projections (2002) and the second author's result for operators with three-point spectrum (2013).
W. Młak (1990)
Annales Polonici Mathematici
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Schôichi Ôta, Franciszek Hugon Szafraniec (2004)
Studia Mathematica
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The paper concerns operators of deformed structure like q-normal and q-hyponormal operators with the deformation parameter q being a positive number different from 1. In particular, an example of a q-hyponormal operator with empty spectrum is given, and q-hyponormality is characterized in terms of some operator inequalities.
Ulrich Groh (1981)
Mathematische Zeitschrift
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Bucur, Amelia (1996)
General Mathematics
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Djordjević, Slaviša V. (1997)
Matematichki Vesnik
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Benharrat, Mohammed, Messirdi, Bekkai (2011)
Serdica Mathematical Journal
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2010 Mathematics Subject Classification: 47A10. We show that the symmetric difference between the generalized Kato spectrum and the essential spectrum defined in [7] by sec(T) = {l О C ; R(lI-T) is not closed } is at most countable and we also give some relationship between this spectrum and the SVEP theory.
S. Djordjević, B. Duggal (2000)
Studia Mathematica
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We show that p-hyponormal operators obey Weyl's and a-Weyl's theorem. Also, we show that the spectrum, Weyl spectrum, Browder spectrum and approximate point spectrum are continuous functions in the class of all p-hyponormal operators.
Andrzej Sołtysiak (1989)
Colloquium Mathematicae
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Slaviša V. Đorđević (1998)
Matematički Vesnik
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Lutz W. Weis (1986)
Extracta Mathematicae
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Chun Guang Li, Ting Ting Zhou (2014)
Studia Mathematica
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A bounded linear operator T acting on a Hilbert space is said to be polaroid if each isolated point in the spectrum is a pole of the resolvent of T. There are several generalizations of the polaroid property. We investigate compact perturbations of polaroid type operators. We prove that, given an operator T and ε > 0, there exists a compact operator K with ||K|| < ε such that T + K is polaroid. Moreover, we characterize those operators for which a certain polaroid type property...
Vladimír Müller (1993)
Studia Mathematica
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We investigate relations between the spectra defined by Słodkowski [14] and higher Shilov boundaries of the Taylor spectrum. The results generalize the well-known relation between the approximate point spectrum and the usual Shilov boundary.
Mohammed Hichem Mortad (2011)
Colloquium Mathematicae
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We present a new approach to the question of when the commutativity of operator exponentials implies that of the operators. This is proved in the setting of bounded normal operators on a complex Hilbert space. The proofs are based on some results on similarities by Berberian and Embry as well as the celebrated Fuglede theorem.
W. Żelazko, Z. Słodkowski (1974)
Studia Mathematica
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